Silicon is a promising anode material for lithium-ion batteries due to its high capacity, but it exhibits significant voltage hysteresis during lithiation and delithiation. This work aims to develop a physics-based model for silicon voltage hysteresis in PyBaMM, eliminating the reliance on empirical open-circuit potential (OCP) fits that lack generalizability and fail to capture phase transformations.

The study begins with a 0D hysteresis model adapted from previous literature, validated by reproducing silicon species evolution and voltage cycling results. The 0D model is then integrated into a 1D composite anode model, where a silicon-graphite (Si-Gr) composite electrode is simulated. Key assumptions include no diffusion within the Si particle (0D), 1D diffusion in the graphite particle, and coupled electrolyte diffusion.

Half-cell testing reveals the effects of hysteresis, particularly under conditions where silicon undergoes crystallization. Extending the model to full-cell simulations with an NMC cathode, the results show that increasing silicon content enhances capacity but also intensifies hysteresis. A transition to a 1D silicon particle model improves accuracy, especially when compared to older empirical OCP functions.

Next steps include further validation with experimental data, integration into PyBaMM to replace empirical OCP functions, and conducting parameter sensitivity analyses. The work demonstrates that a 1D silicon model offers better accuracy and can be more effectively coupled with degradation sub-models, advancing the predictive capability of silicon-based battery modeling.